face diagonals of three non overlapping faces of a cuboid are 2 root 5 cm, 2 root 13 cm and 2 root 10 cm. if this cuboid is melted and recast to form a cube then side of cube generated is equal to
Answers
Given : face diagonals of three non overlapping faces of a cuboid are 2 root 5 cm, 2 root 13 cm and 2 root 10 cm
this cuboid is melted and recast to form a cube
To Find : side of cube generated
Solution:
Let say sides of cuboid are x , y and z
then Diagonal of faces will be
√(x² + y²) , √(x² + z²) , √(y² + z²)
√(x² + y²) = 2√5
=> x² + y² = 20
x² + z² = 52
y² + z² = 40
adding all 2( x² + y² + z² ) = 112
=> x² + y² + z² = 56
z² = 36 => z = 6
y² = 4 => y = 2
x² = 16 => x = 4
Volume of cuboid = 2 * 4 * 6
= 48 cm³
side of cube generated = ∛48 = 3.634 cm
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